With currently operating facilities, dedicated observations of well-selected high redshift QSOs will greatly improve the test of the cosmological model and the study of the dispersion of the \(L_{\rm X}-L_{\rm UV}\)  relation.
eROSITA, flagship instrument of the ongoing Russian Spektrum-Roentgen-Gamma (SRG) mission, will represent an extremely powerful and versatile X-ray observatory in the next decade. The sky of eROSITA will be dominated by the AGN population, with \(\sim \) 3 million AGN at a median redshift of \(z\sim 1\)  expected by the end of the nominal 4-year all-sky survey at the sensitivity of \(F_{0.5-2\,\rm keV} \simeq 10^{-14}\)  erg s\(^{-1}\)  cm\(^{-2}\) , for which extensive multiwavelength follow-up is already planned.
Regarding the constraints on the cosmological parameters (such as \(\Omega _{\rm M}\) , \(\Omega _\Lambda \) , and \(w\) ) through the Hubble diagram of QSOs, we predict that the 4-year eROSITA all-sky survey alone, complemented by redshift and broadband photometric information, will supply the largest QSO sample at \(z<2\)  (average redshift \(z\simeq 1\) , see [1]}), but a relatively small population should survive the Eddington bias cut at higher redshifts (see, e.g., [2]}), thus being available for cosmology [3]} as eROSITA will sample the brighter end of the X-ray luminosity function [4]}.
None the less, the large number of eROSITA QSOs at \(z\simeq 1\)  will be pivotal for both a better cross-calibration of the QSO Hubble diagram with SNe and a more robust determination of \(\Omega _\Lambda \) , which is sensitive to the shape of the low redshift part of the distance modulus–redshift relation.
